cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A244504 Number of distinct lines passing through at least two points in a triangular grid of side n.

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%I A244504 #19 Dec 19 2016 01:41:32
%S A244504 3,9,24,51,102,177,294,459,690,987,1380,1875,2508,3279,4212,5319,6648,
%T A244504 8199,10026,12141,14580,17343,20496,24051,28068,32547,37542,43071,
%U A244504 49218,55983,63456,71661,80658,90447,101100,112635,125160,138675,153252,168915,185784
%N A244504 Number of distinct lines passing through at least two points in a triangular grid of side n.
%H A244504 Heinrich Ludwig, <a href="/A244504/b244504.txt">Table of n, a(n) for n = 2..1000</a>
%F A244504 a(n) = 3*sum(j = 1..n-1, euler_phi(j)*(g(n-j)-g(n-2*j))), where g(i) = i*(i+1)/2 if i > 0, otherwise 0, after _Jon E. Schoenfield_.
%t A244504 g[i_]:=If[i>0,i*(i+1)/2,0]; Table[3*Sum[EulerPhi[j]*(g[n-j]-g[n-2*j]),{j,1,n-1}],{n,2,50}] (* _Vaclav Kotesovec_, Sep 04 2014 after _Jon E. Schoenfield_ *)
%o A244504 (PARI) g(j) = if (j > 0, j*(j+1)/2, 0);
%o A244504 a(n) = 3*sum(j = 1, n-1, eulerphi(j)*(g(n-j)-g(n-2*j))); \\ _Michel Marcus_, Sep 04 2014
%Y A244504 Cf. A234248.
%K A244504 nonn
%O A244504 2,1
%A A244504 _Heinrich Ludwig_, Sep 04 2014